From what I have observed so far, I notice that my piano-playing fingers like to "let go" after they "throw the hammer." This seems to cut out the tone sometimes. If, however, I deliberately make my fingers move fluidly downwards without stopping (which may actually be correct piano technique as well, I never became that advanced at the piano either), then I can produce better tone on the clavichord. It'll take practice. @pianowolfi: I'll try the suggestion. I'll probably try to find more sources on clavichord technique as well.
Since there are no pedals, if I want a pedal-like effect I must hold down several keys at once. This makes for a tactile responsibility for sustain and legato that's actually kind of satisfying.
Another thing I've found so far that is interesting, is playing really dense clusters of tones that one might hear in post-romantic music of all kinds (jazz, atonal, etc.), the clavichord makes all the tones very clear, even in these dense clusters. It actually makes that sort of playing more interesting, for me, than it was on the piano.